/In a trapezium ABCD, AB 11 DC and DC-2AB. If EF is drawn parallel to

1.	/In a trapezium ABCD, AB 11 DC and DC-2AB. If EF is drawn parallel to AB cuts ADin F and BC in E such that BE:EC -3:4. Diagonal DB intersects EF at G. Prove that:7 EF 10AB.
Answer» See diagram. given DC = 2 ABDraw BH parallel to AD. H will be the middle point of DC as AB = DH.Sin EF \|\| AB, FI = AB TheΔBHC andΔBIE are similar as the correspondingsides are parallel.So IE / HC = BE / BC IE = HC * BE / BC = y * 4x/7x = 4 y /7 EF = FI + IE= y + 4 y /7 = 11 y / 7 so 7 EF = 11 AB HIT THE LIKE BUTTON ✔️ 👍

/In a trapezium ABCD, AB 11 DC and DC-2AB. If EF is drawn parallel to AB cuts ADin F and BC in E such that BE:EC -3:4. Diagonal DB intersects EF at G. Prove that:7 EF 10AB.

Answer»

See diagram.

given DC = 2 ABDraw BH parallel to AD. H will be the middle point of DC as AB = DH.Sin EF || AB, FI = AB

TheΔBHC andΔBIE are similar as the correspondingsides are parallel.So IE / HC = BE / BC IE = HC * BE / BC = y * 4x/7x = 4 y /7

EF = FI + IE= y + 4 y /7 = 11 y / 7

so 7 EF = 11 AB

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